Geometric invariants of fanning curves

A Geometric Proof of Removal of Boundary Singularities of Pseudo-Holomorphic Curves

We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting curves with boundary to curves without boundary. Our method is new and geometric and it does not need Sobolev spaces and PDEs.

基于几何力学的弹性曲线

Elastic Curves via Geometric Mechanics

本文从几何力学视角提出弹性曲线的等周刻画，建立保结构的离散弹性曲线理论，为离散空间曲线的哈密顿动力学提供新方法。